Natural boundary condition methods for the microscopic treatment of composite-particle scattering

doi:10.1016/0375-9474(79)90690-0

Nuclear Physics A

Volume 321, Issue 1, 28 May 1979, Pages 171-179

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Abstract

Natural boundary condition methods and the generator coordinate method are used to treat the scattering of composite particles. The procedure is efficient and avoids the instabilities involved in a direct solution of the Hill-Wheeler equation in coordinate space. The method is applied to α-α elastic scattering and the results are compared with other microscopic calculations.

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R-matrix formalism with physical boundary conditions for heavy-ion scattering and application to 24Mg on 24Mg
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An R-matrix formalism for multi-channel scattering problems is developed with special boundary conditions at the matching radius. The boundary conditions in the elastic channels are chosen by means of the phase shifts of the uncoupled problem, while the boundary conditions in the inelastic channels are those of Kapur and Peierls. The method is applied to the elastic scattering and inelastic excitation of ²⁴Mg on ²⁴Mg. The results are compared with coupled channel calculations and experimental data.
Antisymmetrisation effects in composite particle scattering
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Application of an inverse-scattering method to determine the effective interaction between composite particles
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An inverse-scattering method developed recently by Münchow and Scheid is used to determine the effective potential between two α-particles. The α-α scattering phase shifts from a microscopic calculation using the generator coordinate method are employed with the inversescattering technique to obtain a unique, energy-dependent optical potential. A comparison of this potential with the direct (or folded) potential clearly reveals the Pauli exchange effects arising from the inclusion of nuclear exchange between the two a-particles. It is shown that the inverse-scattering approach is accurate for the α-α system even at low energies and should be applicable to heavy-ion systems.
Nucleon exchange effects in 16O-16O elastic scattering
1981, Nuclear Physics, Section A
A natural boundary condition method which was developed recently for the microscopic description of composite particle scattering is used to treat ¹⁶O-¹⁶O elastic scattering. The results of a calculation employing a fully antisymmetric wave function are compared with other microscopic calculations. The effects on the phase shifts of consistently approximating the wave function to allow only up to 1, 2, etc. particle exchange between the clusters, are studied in detail. It is found that in general all the exchange terms contribute significantly although the nature of these exchange effects is dependent upon the choice of the effective nucleon-nucleon interaction.
Calculable methods for many-body scattering
1983, Reviews of Modern Physics

^†: Present address: Department of Physics, The University of Western Australia, Nedlands, WA 6009.

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Nuclear Physics A

Abstract

References (11)

Nucl. Phys.

Nucl. Phys.

Nucl. Phys.

Nucl. Phys.

Nucl. Phys.

Cited by (5)

R-matrix formalism with physical boundary conditions for heavy-ion scattering and application to <sup>24</sup>Mg on <sup>24</sup>Mg

Antisymmetrisation effects in composite particle scattering

Application of an inverse-scattering method to determine the effective interaction between composite particles

Nucleon exchange effects in <sup>16</sup>O-<sup>16</sup>O elastic scattering

Calculable methods for many-body scattering